Finite Group Databasebeta

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C11⋊C5×C22⋊#3861 #44568613

order32340
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×C22⋊#3861
unambiguous semidirect productC22⋊(C11⋊C5×#3861)
unambiguous semidirect productC11⋊(C5×C22⋊#3861)
unambiguous semidirect product(C22×C11⋊C5)⋊#3861
unambiguous semidirect product(C11×C22⋊#3861)⋊C5

Splittings

Fitting, socle, derived, HallC22×C72×C11 ⋊ C3×C5
HallC22×C72×C11⋊C5 ⋊ C3
HallC11×C22⋊#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ A4
HallC72×C11 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ #3861
HallC22×C72 ⋊ C3×C11⋊C5
SylowC72 ⋊ A4×C11⋊C5
HallC22×C11 ⋊ C5×#3861
SylowC11 ⋊ C5×C22⋊#3861
SylowC22 ⋊ C11⋊C5×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C72×C11C3×C5
LCSG ▷ C22×C72×C11
UCSC1

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 315);